Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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I have part A completed but I'm stuck on part B. Are the real solutions the bolded x(t), or are they the x' and y'? Some help would be great thanks!

Consider the system x' = x + 3y y = x - y with initial conditions (0) = 0 and y(0) = 1.² (a) Show that 3 -20 3 +e-2t x(t) = (1² satisfies the initial value problem. (b) Use Euler's method with step size At = 0.5 to approximate this so- lution, and check how close the approximation is to the real solution when t = 2, t = 4, and t = 6. (c) Use Euler's method with step size At = 0.1 to approximate this so- lution, and check how close the approximation is to the real solution when t = 2, t = 4, and t = 6. (d) Discuss how and why the Euler approximations differ from the real solution.
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Transcribed Image Text:Consider the system x' = x + 3y y = x - y with initial conditions (0) = 0 and y(0) = 1.² (a) Show that 3 -20 3 +e-2t x(t) = (1² satisfies the initial value problem. (b) Use Euler's method with step size At = 0.5 to approximate this so- lution, and check how close the approximation is to the real solution when t = 2, t = 4, and t = 6. (c) Use Euler's method with step size At = 0.1 to approximate this so- lution, and check how close the approximation is to the real solution when t = 2, t = 4, and t = 6. (d) Discuss how and why the Euler approximations differ from the real solution.
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